For any positive integer \(d\)  and tetrahedron \(T\) , let \(\mathcal {P}_{d}(T)\)  be the space of all trivariate polynomials defined on \(T\)  with degrees less than or equal to \(d\) . Note that the dimension of \(\mathcal {P}_{d}(T)\)  is \(\binom{d+3}{3}\) .
According to Theorem 15.8 in [1]} and Lemma REF  in Section D.1 in the supplement, the set of Bernstein basis polynomials
\(B^d_T(v):=\lbrace B_{ijkl}^{d,T}(v): i,j,k,l\ge 0, i+j+k+l=d\rbrace \) 
